Sound propagation indoors Sound propagation indoors

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Sound propagation indoors

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Indoors: generalities Indoors: generalities

A sound generated in a closed room produces an acoustic field that results from the superposition of direct waves and reflected waves.

Direct waves come directly from the source to the listener, as in an open field.

Reflected Waves are produced by all the reflections on the walls of the room.

The amount of energy reflected by the boundary surfaces is dependent on their acoustic behavior, described by their coefficients of absorption, reflection and transmission (a, r and t).

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Indoors sound propagation methods Indoors sound propagation methods

Direct Sound

Reflected sound

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r,a,t coefficients (1) r,a,t coefficients (1)

Reflection, absorption and transmission coefficients

The energy balance equation for a wave reflected on a wall is:

• W_o = W_r + W_a + W_t

where W_o is the power of the incoming wave, W_r is the reflected power, W_a is the power absorbed and converted into heat and W_t is the power transmitted through the wall.

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Dividing by W_o we obtain: 1 = r + a + t

where r = W_r/ W_o , a = W_a/ W_o and t = W_t/ W_o are, respectively, the reflection, absorption and transmission coefficients of the wall relative to the incoming acoustic energy.

The value of coefficients r, a, t varies between 0 and 1 0  r,a,t  1 And depends on the material of the wall as well as on frequency and angle of the sound wave.

We can define the apparent acoustic absorption coefficient as

 = 1 – r

Apparent indicates that the acoustic energy going into the wall is only partly absorbed, but does not return in the originating room.

r,a,t coefficients (2)

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Free field, reverberant field, semi-reverberant field Free field, reverberant field, semi-reverberant field

In a closed environment the acoustic field can be of three different kinds:

• Free field

• Reverberant field

• Semi-reverberant field

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Free Field Free Field

A field is defined as free when we are close to the source, where the direct energy component prevails: compared to it, the contribution of all the reflections becomes negligible.

In this case, the field is the same as outdoors, and only depends on source distance and directivity, Q.

The sound pressure level is:

In which L_W is the level of source sound power, Q its directivity, and d is the distance between source and receiver. In a free field, the sound level decreases by 6 dB each time distance d doubles.



 





 

 _w ₂

p 4 d

log Q 10 L

L

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Reverberant field Reverberant field

A field is said to be reverberant if the number of side wall reflections is so elevated that it creates a uniform acoustic field (even near the source).

The equivalent acoustic absorption area of the room is defined as:

(m²)

where  is the average absorption coefficient and S is the total interior surface area (floor, walls, ceiling, etc.)

A reverberant field may be obtained in so called reverberant chambers, where the absorption coefficients of different materials are also measured.

L

_p

 L

_w

10log 4 A



  

  A  

_med

× S

_tot

 

_i

× S

_i

å

i

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Semi-reverberant field (1) Semi-reverberant field (1)

A field is said to be semi-reverberant when at every point the sound field is affected both by the free field and by the reverberant field.

In most normally sized rooms, we can suppose that the acoustic field is semi-reverberant.

In a semi-reverberant acoustic field, the sound energy density at a point is therefore given by the sum of the direct and indirect acoustic fields.

 

 



 

 

 A

4 d

4 log Q 10

L

_p _w ₂

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Semi-reverberant field (2) Semi-reverberant field (2)

Reduction of the sound level in the environment via an acoustic treatment of the walls and ceiling:

• close to the source, the attenuation will be very small, even if the value of A is increased considerably;

• far from the source, (mainly reverberant acoustic field) the sound level reduction can be quite noticeable.

• the straight line (A = ) represents the limit case for a free field (6dB for each doubling of distance d).

• the dotted line marks a zone on whose right the acoustic field is practically reverberant.

Sound propagation indoors Sound propagation indoors